Discounted Cash Flow: Move the Rate and Watch the Value

The calculator below runs a discounted cash flow for Sankalp Industrial Systems Limited, an invented manufacturer. Key in the forecast cash flows, the rate, the terminal assumptions, the bridge and the share count, and it prints every component, its sign and the running total. Discounting at 12.00 per cent and growing forever at 5.00 per cent, the figures it opens on return Rs 2,128.14 crore and Rs 84.41 a share.

Run the Model on Figures Entered by Hand

Once the forecast is agreed, a discounted cash flow has two inputs left that anybody can argue with, and both sit in the terminal block. Putting those two on perpendicular axes is not a presentation choice, it is the shape of the problem: the answer is a surface rather than a point, and it tilts far more steeply in one direction than the other. Everything below walks that surface. Its construction, the projection of each forecast line, and the derivation of the 12.00 per cent rate are each covered separately.

What Does the Grid Hold Fixed?

To the rupee, the default enterprise value is Rs 21,28,13,79,094, and even that is a rounded print of a longer number. Where roughly four fifths of an answer has come out of one formula, the closing digits are noise.

Five things are fixed before the reader touches anything. The forecast is not on the table here, and knowing which inputs are shut is as much a part of reading a model as knowing which are open.

Cash flows are in rupees crore. A 25.0 per cent effective tax charge is assumed by this invented forecast and is already inside those five cash flows, so the reader never sets it. Operating profit after taxTake trading profit, deduct a tax charge, and stop there. No interest has gone through the line yet, so whoever lent the company money is still waiting at this point in the sum. matters here only because the terminal block is built from the Year 5 figure rather than from the Year 5 cash flow.

Enterprise value in rupees crore, on the two axes. Rows are the cost of capital and columns the terminal growth rate.

The answer falls down every column and climbs across every row, and the two movements are not the same size. The asymmetry between the two axes is the first thing worth taking from the grid.

What Does One Whole Point on the Rate Cost?

Hold the terminal growth rate at 5.00 per cent and walk down the rate axis. At 11.00 per cent the answer is Rs 2,506.58 crore. At 12.00 per cent it is Rs 2,128.14 crore. At 13.00 per cent it is Rs 1,845.06 crore. One whole point on the cost of capital takes Rs 283.08 crore out of the answer, 13.30 per cent of it.

Think of a household working out what a promised inheritance is worth today. The rate they mentally charge for the wait applies to every year rather than once, including the year the terminal block lands in. So it shrinks the near payments a little and the far ones a great deal. The terminal block is the most distant object in the model.

Why Is the Growth Axis the Weaker of the Two?

Now hold the rate at 12.00 per cent and walk across. At 4.00 per cent growth the answer is Rs 2,017.49 crore and at 6.00 per cent it is Rs 2,272.83 crore. One whole point on the terminal growth rate adds Rs 144.69 crore, 6.80 per cent. The rate is close to twice as powerful as growth on this company.

The reason is structural. Terminal growth touches one term in the sum; the cost of capital touches every term, and it touches the terminal term twice, once in the divisor of the perpetuityA stream with no last payment. The far end of it is discounted down to almost nothing, so its value stays finite anyway. and once in the five year discount that brings it back. Growth is the number people argue about in meetings, so most readers guess the other way round.

How DCF Assumptions Affect Valuation Range

The twenty five cells run from Rs 1,773.03 crore in the low corner, at a 13.00 per cent rate and 4.00 per cent growth, to Rs 2,746.04 crore in the high corner, at 11.00 per cent and 6.00 per cent. The span is Rs 973.01 crore, or 54.88 per cent of the low corner, produced entirely by moving two assumptions two points each and touching nothing about the business.

Sankalp Industrial Systems Limited has a traded enterprise value of Rs 2,240.00 crore, and that figure sits inside the span. A traded figure landing inside a span settles nothing. Several assumption pairs in the grid produce it, and no arithmetic in the grid can say which pair the buyers and sellers were using.

A span that wide is the model reporting how much of its own answer came from two assumptions rather than from the company. A published range that names its assumption pairs is doing its job; a single figure quoted without them hides the same span behind two decimal places.

The Per Share Panel: One Subtraction and One Division

The per share grid is not a second model. Every enterprise value in the table above becomes a per share figure by taking off a net bridge of Rs 440.00 crore and dividing by 20.00 crore shares, and nothing else changes. The bridge is the same in every cell because not one of its four lines depends on the discount rate.

Gross debtAdd up every borrowing and stop. Cash the company happens to be holding is not netted off first. comes out at Rs 600.00 crore rather than net debt, because the Rs 120.00 crore of cash was added on the line above and taking net debt off as well would count it twice. Minority interestThe slice of a consolidated subsidiary that outside holders keep. The outside holders' slice leaves the sum on the way to a share price, because the slice is somebody else's claim. of Rs 60.00 crore comes out because the forecast consolidated all of Sankalp Coatings Private Limited, while only three quarters of it belongs to the group.

Value per share in rupees, on the same two axes.

The Non-Operating Asset Line in the Bridge

Two things on the balance sheet of Sankalp Industrial Systems Limited produce none of the cash flow the grid discounts: a surplus land parcel at Rs 45.00 crore and the 26.0 per cent holding in Aruna Tooling Private Limited at Rs 55.00 crore. Together they are Rs 100.00 crore. Because neither one produced a rupee of the forecast, neither can be inside the enterprise value, so both are added afterwards at their own carrying figure.

Taking the line out in the calculator is worth doing once. With it, equity value is Rs 1,688.14 crore and Rs 84.41 a share. Without it, equity value is Rs 1,588.14 crore and Rs 79.41 a share. Rs 5.00 a share is what those two items are contributing, and a model that forgets the line has quietly given the land and the holding away.

How Much of the Answer Is Terminal Value?

At the default the five forecast years contribute Rs 468.41 crore of present value and the terminal block contributes Rs 1,659.72 crore. Terminal value accounts for 77.99 per cent of what the model returns, leaving the five explicit years barely a fifth of it between them. The terminal share is printed inside every cell of the calculator, so a reader watching the value move also watches how much of the value is coming out of one formula.

The share is not constant across the grid. At an 11.00 per cent rate with 6.00 per cent growth it reaches 82.47 per cent; at 13.00 per cent with 4.00 per cent growth it drops to 74.29 per cent. Discounting punishes distance, so a lower rate spares the terminal block more than it spares Year 1, and the consequence is worth sitting with: the cheaper this company's capital is believed to be, the more of the answer comes out of an assumption about forever.

Operating Cash Flow vs Free Cash Flow: What the Grid Discounts

The numerator here is free cash flow to the firm, not the cash from operations line at the top of a cash flow statement, and the two are different objects. The cash flow statement's operating section still has interest inside it in most presentations and has not yet paid for a single machine, so discounting it at a cost of capital would double count the lenders and ignore the capital expenditure.

Free cash flow to the firm strips both problems out: it is operating profit after tax, add back depreciationThe accounting charge that spreads the cost of a long lived asset over the years it is used, rather than in the year it was paid for., less capital expenditureMoney spent on plant, machinery and buildings, which leaves as cash in the year it is spent whatever the profit line decides to do with it., less the movement in net working capitalGoods on the shelf plus invoices buyers have still to pay, netted against invoices the business has itself not yet settled.. The full definition, and whose claim the resulting cash answers to, is set out under free cash flow to the firm.

The Bull Case Preset, and Why It Is Not a Cell

The bull setting moves four assumptions together: the annual increase in revenue rises from Rs 120.00 crore to Rs 150.00 crore, the margin from 24.0 to 25.0 per cent, the rate falls to 11.50 per cent and terminal growth rises to 5.50 per cent. Enterprise value is Rs 2,626.89 crore, 23.44 per cent above the default. Two of the four changes rebuild the forecast itself rather than the discounting of it, so that enterprise value cannot be reached by dragging either axis.

A sensitivity and a scenario part company here. Dragging one axis asks what happens if I was wrong about the rate. A preset asks what happens if I was wrong about the business, and a different business throws off a different sheet of cash flows. Load the bull forecast into the fields above and the five cash flows change with it.

The Bear Case Preset, and the Cash It Frees Early

The bear setting takes revenue growth down to Rs 80.00 crore a year, the margin to 22.5 per cent, the rate up to 12.50 per cent and terminal growth down to 4.00 per cent. Enterprise value is Rs 1,654.94 crore, 22.24 per cent below the default. There is a surprise buried in it. A company growing more slowly has less growth to pay for, so the bear case throws off more cash in Year 1 than the default does, Rs 115.93 crore against Rs 98.00 crore.

A street vendor who decides not to open a second cart has more money in the tin this month, not less. The cash given up comes later, and in a discounted cash flow the whole of that giving up lands in the terminal block. Slower growth is not less cash now. Slower growth is less cash forever.

Two-Stage Is All This Grid Is, and It Is a Choice

The model behind every cell has two stages and no more: five explicit years, then one growth rate applied forever. A two stage build assumes the company steps from its Year 5 growth of about 7.14 per cent straight down to 5.00 per cent on the first day of Year 6, with no in between. Nothing in the arithmetic objects to that; it is simply what the shape assumes.

What a Three-Stage DCF Would Need That This One Does Not Carry

A third stage inserts a fading period between the explicit years and the perpetuity, over which growth glides from the forecast rate down to the terminal rate. Building one needs three things this record does not settle: how many fading years, what path the growth takes across them, and what the return on new invested capitalLook only at money put in this year and ask what it earns once it is working. Older capital, installed long ago and already producing, is a separate question. does while that fading happens. The calculator refuses to add a third stage rather than invent those three, and the refusal is the honest answer: a model that quietly supplies missing assumptions is worse than one that stops.

Reverse DCF: Enter a Value and Read Out the Assumption

Run the other way, the model takes a value and returns an assumption. Sankalp Industrial Systems Limited has a traded enterprise value of Rs 2,240.00 crore. Fed in, that figure produces two answers, not one. Holding the rate at 12.00 per cent, that value needs terminal growth of about 5.80 per cent; holding growth at 5.00 per cent, it needs a rate of about 11.67 per cent.

One equation carries two unknowns, so two answers come back. Fix either input and the other is determined. No single assumption pair sits behind a value, and a backward run that fails to say which input it held has said nothing. Calling an assumption high, low, generous or stretched is a judgement rather than arithmetic, so the tool prints the assumption and stops there.

DCF vs Reverse DCF: One Model Run in Two Directions

The two runs use identical arithmetic and answer opposite questions, and the output of the backward run is an assumption rather than a verdict.

How to Choose a Discounting Convention

Year-end discounting places the whole of a year's cash at that year's closing point, as though nothing had been collected until then. Mid-year discounting treats it as arriving evenly through the year. Even collection is closer to how a business actually takes money in. Year-end is the convention used throughout the grid and the calculator. Switching the convention changes nothing whatever about the company: it changes an assumption about when inside each year the cash is treated as landing.

The size of it is settled for the explicit period and is worth seeing. Year-end, those five cash flows are worth Rs 468.41 crore today. Mid-year, they are worth Rs 495.72 crore, a lift of 5.83 per cent, and that figure is no accident: it is 1.12 raised to the power of one half, less one. Where the terminal block lands under the other convention is not settled by this record, so the calculator moves the explicit period, prints the difference, and declines to restate the enterprise value. A tool that guessed the rest would be inventing a figure and calling it a convention.

Historical Financials or Forward: Which Base the Multiple Is Quoted On

The calculator prints the multiple its own answer implies, and there are two ways to print it. Take Year 0 earnings measured above interest, above tax and above the charges for wear, Rs 288.00 crore, and the default answer of Rs 2,128.14 crore is 7.39 times it. Against the Year 1 figure of Rs 316.80 crore it is 6.72 times. Nothing about the valuation moved, only the denominator, and a multiple quoted without saying which base it used is not a number anybody can use.

The same trap catches the traded side. The traded enterprise value of Rs 2,240.00 crore is 7.78 times on a historical base and 7.07 times on the forward one. Comparing a forward multiple against a historical one on a growing company will make the first look cheap every time, purely because the two are measuring different years.

What Will the Calculator Not Allow?

Honesty in a tool is mostly a matter of which cells it hands over and which it keeps back, and a reader who cannot tell them apart cannot judge the output. Four locks are in place here and each has its reason printed beside it.

The five forecast cash flows belong to a forecast built separately, so the grid shuts them. The panel above opens those same five fields, because up there the figures belong to the reader rather than to the worked case. Terminal reinvestment is growth divided by the return on new capital, so 5.00 over 18.00 gives 27.78 per cent, and unhooking the two would let a reader assume 6.00 per cent growth forever while reinvesting as though growth were 4.00. Terminal growth at or above the discount rate leaves the perpetuity with no finite value. Both panels stop there rather than printing whatever the divisor produces.

How Do a Lender, an Analyst and a Committee Each Read One Grid?

A lender looking at Sankalp Industrial Systems Limited reads the bottom left. A credit officer asks not what the business is worth on a good day but whether there is cover on a bad one. So the cell at a 13.00 per cent rate and 4.00 per cent growth, Rs 1,773.03 crore, is the one that matters, and it gets compared against gross debt of Rs 600.00 crore. A lender uses a valuation grid to find the floor, not the answer.

An equity analyst does the opposite: pick one pair, defend it in writing, and publish the cell that follows, with the pair printed beside the number so a reader can disagree with the assumption rather than with the arithmetic. Publishing the grid instead of a cell looks thorough and is a refusal to take a view.

An investment committee uses it as a question generator: ask which cell the recommendation rests on, then ask what would have to change about the business before the cell next door became the right one. Here the second answer is crisp. Moving from the default to the traded enterprise value of Rs 2,240.00 crore requires either about 80 basis points more terminal growth or about 33 basis points less on the rate, and that is a conversation people can have.

A household squinting at a home loan sheet is running the same exercise under another name. Rate down one side, repayment period across the top, an instalment in every box: two assumptions, one consequence, a table of answers. Reading only the middle box misses what the table was printed for.

Sankalp Industrial Systems Limited, Sankalp Coatings Private Limited and Aruna Tooling Private Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.